On $g μ$-Paracompact Sets (European Journal of Pure and Applied Mathematics, 2025)
In this work, we use the notion of the $g μ$-paracompact space \cite{ADeb} to introduce two types of $g μ$-paracompact sets called $α$-$g μ$-paracompact and $β$-$g μ$-paracompact. We show that every $α$-$g μ$-paracompact set is $β$-$g μ$-paracompact and if a generalized topological space $(S,μ)$ is $g μ$-paracompact, then every $μ$-closed subset in $(S,μ)$ is $α$-$g μ$-paracompact while every $μ g$-closed subset in $(S, μ)$ is $β$-$g μ$-paracompact. Finally, we introduce the notion of $co$-$α$-$gμ$-paracompact set as an application of $α$-$gμ$-paracompact and study some of its features.
Keywords: $\gm-paracompact; $α gm-paracompact set; $β gm-paracompact set